Sensitivity Analysis of SAR Estimators
AbstractEstimators of spatial autoregressive (SAR) models depend in a highly non-linear way on the spatial correlation parameter and least squares (LS) estimators cannot be computed in closed form. We first compare two simple LS estimators by distance and covariance properties and then we study the local sensitivity behavior of these estimators using matrix derivatives. These results allow us to calculate the Taylor approximation of the least squares estimator in the spatial autoregression (SAR) model up to the second order. Using Kantorovich inequalities, we compare the covariance structure of the two estimators and we derive efficiency comparisons by upper bounds. Finally, we demonstrate our approach by an example for GDP and employment in 239 European NUTS2 regions. We find a good approximation behavior of the SAR estimator, evaluated around the non-spatial LS estimators. These results can be used as a basis for diagnostic tools to explore the sensitivity of spatial estimators.
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Bibliographic InfoPaper provided by Institute for Advanced Studies in its series Economics Series with number 262.
Length: 19 pages
Date of creation: Jan 2011
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Find related papers by JEL classification:
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
- R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-01-30 (All new papers)
- NEP-ECM-2011-01-30 (Econometrics)
- NEP-GEO-2011-01-30 (Economic Geography)
- NEP-URE-2011-01-30 (Urban & Real Estate Economics)
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- Liu, Shuangzhe & Ma, Tiefeng & Polasek, Wolfgang, 2012.
"Spatial System Estimators for Panel Models: A Sensitivity and Simulation Study,"
294, Institute for Advanced Studies.
- Shuangzhe Liu & Tiefeng Ma & Wolfgang Polasek, 2013. "Spatial System Estimators for Panel Models: A Sensitivity and Simulation Study," Working Paper Series 05_13, The Rimini Centre for Economic Analysis.
- Shuangzhe Liu & Tiefeng Ma & Wolfgang Polasek, 2012. "Spatial System Estimators for Panel Models: A Sensitivity and Simulation Study," Working Paper Series 75_12, The Rimini Centre for Economic Analysis.
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